# The side length of an equilateral triangle is 20cm. How do you find the length of the altitude of the triangle?

Jul 9, 2018

I tried this:

#### Explanation:

Consider the diagram:

we can use Pythgoras theorem applied to the blue triangle giving:

${h}^{2} + {10}^{2} = {20}^{2}$

rearranging:

$h = \sqrt{{20}^{2} - {10}^{2}} = \sqrt{300} = 17.3 c m$

Jul 9, 2018

$17.3 c m$

#### Explanation:

You can use trigonometry to find the altitude (same as height) of the triangle.

In an equilateral triangle, all the sides are equal and all the angles are equal to 60°

The altitude is the side opposite the 60° angle

o/20 = sin 60°

o = 20 xx sin60°

$o = 17.3 c m$